Testing for a unit root in a random coefficient panel data model

This paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model, in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance. The asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples.     

Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances

Abstract

This paper develops a unified framework for fixed effects (FE) and random effects (RE) estimation of higher-order spatial autoregressive panel data models with spatial autoregressive disturbances and heteroscedasticity of unknown form in the idiosyncratic error component. We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define both an RE and an FE spatial generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators and derive their joint asymptotic distribution, which is robust to heteroscedasticity of unknown form in the idiosyncratic error component. Finally, we derive a robust Hausman test of the spatial random against the spatial FE model.     

General Bayesian time-varying parameter vector autoregressions for modeling government bond yields

US yield curve dynamics are subject to time-variation, but there is ambiguity about its precise form. This paper develops a vector autoregressive (VAR) model with time-varying parameters and stochastic volatility, which treats the nature of parameter dynamics as unknown. Coefficients can evolve according to a random walk, a Markov switching process, observed predictors, or depend on a mixture of these. To decide which form is supported by the data and to carry out model selection, we adopt Bayesian shrinkage priors. Our framework is applied to model the US yield curve. We show that the model forecasts well, and focus on selected in-sample features to analyze determinants of structural breaks in US yield curve dynamics.     

Modelling optimal strategies for the allocation of wealth in multicurrency investments

This paper analyzes rates of return on financial assets denominated in five major currencies and provides a framework for the determination of optimal strategies for the allocation of wealth in multicurrency investments. Three models are estimated: a univariate autoregressive conditional heteroskedasticity (ARCH) model, an extended ARCH model using the random coefficient (RC) procedure, and a pure RC model. A comparison of the forecasts of these models with those generated by a random walk model demonstrates that forecasts based on the RC/extended ARCH procedure are superior to those based on the random walk model and those based on direct ARCH estimation. These results could be useful for both international investors for the allocation of their wealth among fixed-income investment securities and central banks for the management of their external reserve assets.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

Model identification for infinite variance autoregressive processes

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.     

The sampling distributions of the predictor for an autoregressive model under misspecifications

Approximations to the sampling distributions of the predictor are given misspecifying the autoregressive moving average model as an autoregressive model. We deal with both conditional and unconditional distributions for the dependent and independent cases according to whether the sample data used in estimation and in prediction are dependent or not. The bias and mean squared error are easily obtained from these approximations.     

Random‐coefficient periodic autoregressions

We propose a new periodic autoregressive model for seasonally observed time series, where the number of seasons can potentially be very large. The main novelty is that we collect the periodic coefficients in a second‐level stochastic model. This leads to a random‐coefficient periodic autoregression with a substantial reduction in the number of parameters to be estimated. We discuss representation, parameter estimation, and inference. An illustration for monthly growth rates of US industrial production shows the merits of the new model specification.     

The RWDAR model: A novel state-space approach to forecasting

This paper introduces the Random Walk with Drift plus AutoRegressive model (RWDAR) for time-series forecasting. Owing to the presence of a random walk plus drift term, this model shares some similarities with the Theta model of Assimakopoulos and Nikolopoulos (2000). However, the addition of a first-order autoregressive term in the state equation provides additional adaptability and flexibility. Indeed, it is shown that RWDAR tends to outperform the Theta model when forecasting both stationary and nearly non-stationary time series. This paper also proposes a simple estimation method for the RWDAR model based on the solution of the algebraic Riccati equation for the prediction error covariance of the state vector. Simulation results show that this estimator performs as well as the standard Kalman filter approach. Finally, using yearly data from the M3 and M4 competition datasets, it is found that RWDAR outperforms traditional forecasting methods.     

Testing the autoregressive parameter with the t statistic

This paper considers a Gaussian first-order autoregressive process with unknown intercept where the initial value of the variable is a known constant. Monte Carlo simulations are used to investigate the sampling distribution of the t statistic for the autoregressive parameter when its value is in the neighborhood of unity. A small sigma asymptotic result is exploited in the construction of exact non-similar tests. The powers of non-similar tests of the random walk and other hypotheses are estimated for sample sizes typical in economic applications.     

Pooling data for the analysis of dynamic marketing systems

Vector autoregressive (VAR) models have become popular in marketing literature for analyzing the behavior of competitive marketing systems. One drawback of these models is that the number of parameters can become very large, potentially leading to estimation problems. Pooling data for multiple cross-sectional units (stores) can partly alleviate these problems. An important issue in such models is how heterogeneity among cross-sectional units is accounted for. We investigate the performance of several pooling approaches that accommodate different levels of cross-sectional heterogeneity in a simulation study and in an empirical application. Our results show that the random coefficients modeling approach is an overall good choice when the estimated VAR model is used for out-of-sample forecasting only. When the estimated model is used to compute Impulse Response Functions, we conclude that one should select a modeling approach that matches the level of heterogeneity in the data.     

Random walks,cointegration, and the transmission of shocks across global real estate and equity markets

This article presents tests of the random walk hypothesis for the U.S. and world commercial real estate markets along with the world stock market through utilizing appropriate market indices. The augmented Dickey-Fuller and Phillips-Perron unit root tests and Cochrane variance ratio test find each of these markets to exhibit random walk behavior. In addition, Johansen-Juselius cointegration tests reveal that the three markets are not cointegrated. The vector autoregressive model shows little or no predictive power in explaining the variation in monthly returns. The generalized impulse response functions suggest that shocks stemming from one market are quickly disseminated to the other markets within two months. (JEL G14, G15)     

Optimal transformations for categorical autoregressive time series

This paper describes a method for finding optimal transformations for analyzing time series by autoregressive models. 'Optimal' implies that the agreement between the autoregressive model and the transformed data is maximal. Such transformations help 1) to increase the model fit, and 2) to analyze categorical time series. The method uses an alternating least squares algorithm that consists of two main steps: estimation and transformation. Nominal, ordinal and numerical data can be analyzed. Some alternative applications of the general idea are highlighted: intervention analysis, smoothing categorical time series, predictable components, spatial modeling and cross-sectional multivariate analysis. Limitations, modeling issues and possible extensions are briefly indicated.     

A flexible approach to parametric inference in nonlinear and time varying time series models

Many structural break and regime-switching models have been used with macroeconomic and financial data. In this paper, we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications. We build on earlier work showing the relationship between flexible functional forms and random variation in parameters. Our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring (reordered) observations. The range of priors produced in this way can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the amount of random variation in parameters to depend on the distance between (reordered) observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). Bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering. Conditional on a hypothetical reordering and distance function, a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation. We use artificial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth.     

Price competition in the spatial real estate market: allies or rivals?

This paper examines whether real estate firms can avoid price competition when properties in the vicinity are priced by allies. An oligopoly model with differentiated products generally suggests that real estate firms engage in price competition with their spatially closest rivals. Yet, they can raise property prices when the market share of their allies increases. To test this prediction, a spatial autoregressive model with spatial autoregressive disturbances, including a share of allies in the vicinity, is estimated using data on the prices of residential condos in central Tokyo, Japan. The model prediction is supported by the empirical results. In the data set, the magnitude of the market share on property prices increases with the expansion of the size of the spatial market.     

Semiparametric time series regression modeling with a diverging number of parameters

Variable selection and error structure determination of a partially linear model with time series errors are important issues. In this paper, we investigate the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation penalty for a partially linear model with a divergent number of covariates and finite order autoregressive time series errors. Both consistency and asymptotic normality of the proposed penalized estimators are derived. The oracle property of the resultant estimators is proved. Simulation studies are carried out to assess the finite‐sample performance of the proposed procedure. A real data analysis is made to illustrate the usefulness of the proposed procedure as well.     

A link between random coefficient autoregressive models and some agent based models

An agent based model (ABM), where each agent makes decisions by using the sum of two signals, is proposed. The first is related to the fundamental information while the second comes from trader’s idiosyncratic noise. This model entails the switching between two groups called fundamentalist and noise traders. Additionally, if the price impact function is log-linear, then the dynamic of log asset prices belongs to the class of random coefficient autoregressive RCA(p) models, which are known to share important stylized facts of financial prices.     

Bayesian Variable Selection in Spatial Autoregressive Models

This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. It presents two alternative approaches that can be implemented using Gibbs sampling methods in a straightforward way and which allow one to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. A simulation study shows that the variable selection approaches tend to outperform existing Bayesian model averaging techniques in terms of both in-sample predictive performance and computational efficiency. The alternative approaches are compared in an empirical application using data on economic growth for European NUTS-2 regions.     

Multivariate dynamic intensity peaks-over-threshold models

We propose a multivariate dynamic intensity peaks-over-threshold model to capture extremes in multivariate return processes. The random occurrence of extremes is modeled by a multivariate dynamic intensity model, while temporal clustering of their size is captured by an autoregressive multiplicative error model. Applying the model to daily returns of three major stock indexes yields strong empirical support for a temporal clustering of both the occurrence and the size of extremes. Backtesting value-at-risk and expected shortfall forecasts shows that the consideration of clustering effects and of feedback between the magnitudes and the intensity of extremes results in better forecasts of risk.     

Power of Tests for Unit Roots in the Presence of a Linear Trend*

Dickey and Fuller [Econometrica (1981) Vol. 49, pp. 1057–1072] suggested unit‐root tests for an autoregressive model with a linear trend conditional on an initial observation. TPower of tests for unit roots in the presence of a linear trendightly different model with a random initial value in which nuisance parameters can easily be eliminated by an invariant reduction of the model. We show that invariance arguments can also be used when comparing power within a conditional model. In the context of the conditional model, the Dickey–Fuller test is shown to be more stringent than a number of unit‐root tests motivated by models with random initial value. The power of the Dickey–Fuller test can be improved by making assumptions to the initial value. The practitioner therefore has to trade‐off robustness and power, as assumptions about initial values are hard to test, but can give more power.